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The phase stability of Al-containing cubic transition metal (TM) nitrides, where Al substitutes for TM (i.e. TM1−x Al x N), is studied as a function of the TM valence electron concentration (VEC). X-ray diffraction and thermal analyses data of magnetron sputtered Ti1−x Al x N, V1−x Al x N and Cr1−x Al x N films indicate increasing phase stability of cubic TM1−x Al x N at larger Al contents and higher temperatures with increasing TM VEC. These experimental findings can be understood based on first principle investigations of ternary cubic TM1−x Al x N with TM = Sc, Ti, V, Cr, Y, Zr and Nb where the TM VEC and the lattice strain are systematically varied. However, our experimental data indicate that, in addition to the decomposition energetics (cubic TM1−x Al x N → cubic TMN + hexagonal AlN), future stability models have to include nitrogen release as one of the mechanisms that critically determine the overall phase stability of TM1−x Al x N.

We describe a new approach to modelling pearlescent paints based on decomposing paint layers into stacks of imaginary thin sublayers. The sublayers are chosen so thin that multiple scattering can be considered across different sublayers, while it can be neglected within each of the sublayers. Based on this assumption, an efficient recursive procedure of assembling the layers is developed, which enables to compute the paint BRDF at interactive speeds. Since the proposed paint model connects fundamental optical properties of multi‐layer pearlescent and metallic paints with their microscopic structure, interactive prediction of the paint appearance based on its composition becomes possible.

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A generalized two-disk dynamo model is considered that includes mechanical friction; this model is intended to simulate in its broad character the behavior of the geodynamo. Fixed points, limit cycles and chaotic attractors are located for different input parameters of the model. The chaotic regimes are of several kinds as are the "routes to chaos". Several approximate models, helpful for studying the dynamo are discussed. A number of essential differences from the well-known Rikitake dynamo are demonstrated.